Assistance finding the area between curves

Question

I need your help in finding the area between the following graphs.

y=e^x, y=x^2 - 1, x=-1, and x=1

Answer 1

Graphing these you get this:

The area between the curves is obviously the integral. You can see that the area is broken into 2 parts. To find out where they intersect, it's best to use a graphing calculator to find the point. x² = e^x cannot easily be solved using algebra. The intersection point is approx x = -.703467. So you can divide the integrals into 2 parts, from -1 to -0.703467 and in that integral do ∫(x² - e^x)dx then in the second integral from -0.703467 to 1 and in that integral do ∫(e^x - x²)dx and add the results together.